格子玻尔兹曼方法模拟弯流道中粒子的惯性迁移行为

本文发展了一个能够模拟微流场环境下粒子惯性迁移行为的三维耦合模型.该模型采用基于动理论的格子玻尔兹曼方法(LBM)描述流体流动,采用牛顿动力学模型描述粒子的平动和转动,采用基于LBM反弹格式的运动边界法实现流体与粒子模型的耦合.模拟了重力作用下粒子的沉降过程和Couette流条件下粒子的转动过程,通过将模拟结果与文献中的基准解进行对比定量验证了模型的可靠性.模拟了不同大小的球形粒子在环形流道中的迁移,成功复现了经典的流道截面二次流形成过程,分析了粒径大小对粒子在流道中平衡位置的影响机理.结果表明,粒子在弯流道中的平衡位置与粒径大小密切相关,小半径粒子的平衡位置靠近流道外侧而大半径粒子则靠近流道内侧.通过实验对模拟结果进行了定性验证.本模型为深入研究微流场环境下粒子的运动特性以及开发微流控粒子分选器件提供了参考依据.     

Dynamics of a self-propelled particle under different driving modes in a channel flow

In this paper, a model that combines the lattice Boltzmann method with the singularity distribution method is proposed to simulate a self-propelled particle swimming(exhibiting translation and rotation) in a channel flow. The results show that the velocity distribution for a self-propelled particle swimming deviates from a Maxwellian distribution and exhibits highvelocity tails. The influence of an eccentric potential doublet on the translation velocity of the particle is significant. The velocity decay process can be described using a double exponential model form. No large differences in the velocity distribution were observed for different translation Reynolds numbers, rotation Reynolds numbers, or regular intervals.     

微通道内椭球颗粒惯性聚焦行为数值研究

基于浸没边界-格子Boltzmann方法,对方形截面微通道内椭球颗粒的惯性迁移与旋转动力学行为进行数值研究,发现微通道内椭球颗粒的惯性迁移存在两种主要的运动状态：①翻转状态,即椭球颗粒前进过程中长轴始终在中心对称平面内;②滚动状态,即椭球颗粒前进过程中长轴始终垂直于中心对称平面.研究表明：在低Re数（Re=10）下颗粒以两种状态随流体迁移至平衡位置;在较大Re数（50≤Re≤200）下最终均以翻转状态随流体迁移,随Re数增加,平衡位置先逼近壁面后远离壁面.通过对不同运动状态下椭球颗粒周围的微观流场进行分析,提示该微观流动在颗粒惯性聚焦行为特征中有重要影响,并从流体和颗粒的惯性角度对颗粒不同运动状态的转换机理给出解释.     

粒子在锥形管中运动的晶格玻尔兹曼方法研究

运用晶格玻尔兹曼方法对单个悬浮粒子在锥形管中的运动进行了数值计算, 给出了锥形管流体的速度分布和压力分布等. 粒子所受的流体作用力分别用动量交换法、改进的动量交换法和压力张量积分法进行计算. 分析了在不同初始位置释放的粒子的运动轨迹和速度变化情况, 结果表明压力张量积分法和改进的动量交换法的计算结果一致, 而没有改进的动量交换法的计算结果和前两者略有不同. 关键词： 晶格玻尔兹曼方法 锥形管 悬浮粒子 改进的动量交换法     

Multi-relaxation time lattice Boltzmann simulation of inertial secondary flow in a curved microchannel

The inertial secondary flow is particularly important for hydrodynamic focusing and particle manipulation in biomedical research.In this paper,the development of the inertial secondary flow structure in a curved microchannel was investigated by the multi relaxation time lattice Boltzmann equation model with a force term.The numerical results indicate that the viscous and inertial competition dominates the development of secondary flow structure development.The Reynolds number,Dean number,and the cross section aspect ratio influence significantly on the development of the secondary vortexes.Both the intensity of secondary flow and the distance between the normalized vortex centers are functions of Dean numbers but independent of channel curvature radius.In addition,the competition mechanism between the viscous and inertial effects were discussed by performing the particle focusing experiments.The present investigation provides an improved understanding of the development of inertial secondary flows in curved microchannels.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

Study of force-dependent and time-dependent transition of secondary flow in a rotating straight channel by the lattice Boltzmann method

A numerical study using the lattice Boltzmann method has been carried out for flow through a rotating straight channel with a rectangular cross section. With different forces applied, the secondary flow exhibits two-cell states, four-cell states or six-cell states at a range of low rotational Reynolds number, however, within which only the two-cell states have been commonly reported. In addition to the force-dependent flow transition, a time-dependent flow transition of the secondary flow among two-cell states, four-cell states and six-cell states is also discovered during flow development. These newly found flow transitions and their regulations by force application have been analyzed. Based on numbers of case studies, it is found that a dimensionless number, the ratio of the driving pressure gradient to the centrifugal force, regulates such flow transitions. This study not only releases new phenomena of flow transition, but also indicates new applications in flow control, particle separation and heat transfer.     

疏水表面滑移流动及减阻特性的格子Boltzmann方法模拟

采用格子Boltzmann方法研究了固体壁面对流体的作用强度与其润湿性的关系,在此基础上进一步模拟了疏水表面微通道内的流体流动,获得了润湿性对疏水表面滑移流动及减阻特性的影响规律,证实了疏水表面表观滑移的存在性并揭示了其产生机理.结果表明,疏水性作用在疏水表面的近壁区诱导了一个低密度层,而表观滑移则发生在低密度层上.表观滑移是疏水表面具有减阻作用的直接原因,减阻效果随滑移长度的增大而增大.对于特定的流体系统,滑移长度是疏水表面的固有属性,仅是壁面润湿性的单一函数,而与流动本身的性质无关.     

非对称弯曲微流道中粒子惯性聚焦动态过程及流速调控机理研究

设计制作了一种具有非对称弯曲微流道结构的微流控芯片, 搭建实验平台定量表征聚苯乙烯粒子和血细胞沿流道的动态惯性聚焦过程, 并系统研究了流体流速和粒子尺寸对粒子聚焦特性的调控机理. 通过分析粒子荧光图谱和对应量化强度曲线, 将粒子沿流道长度的横向迁移过程分为形成聚焦和平衡位置调整两个阶段, 指出在整个聚焦过程中具有小曲率半径的流道结构起主导作用. 根据全流速段内粒子聚焦特性的演变, 重点分析潜在惯性升力和Dean 曳力的竞争机制, 提出了阐述粒子聚焦流速调控过程的三阶段模型. 进一步比较两种尺寸粒子聚焦位置和聚焦率随流速与流道长度的变化规律, 发现大粒子具有更好的聚焦效果和稳定性, 且两种粒子的相对位置可通过流速进行调整. 最后, 通过分析血细胞在非对称弯流道中的横向迁移特性, 验证了粒子惯性聚焦机理在复杂生物粒子操控方面的适用性. 上述结论为深入研究微流体环境下粒子的运动特性以及开发微流式细胞术等临床即时诊断器件提供了重要参考.     

利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流

利用格 子 Boltzmann方法模拟矩形腔内纳米流体Rayleigh-Benard对流, 得到温度场和流线分布, 比较分析不同Ra数、体积分数、粒径下纳米流体对流换热的变化情况. 结果表明: 在相同的Ra 数和体积分数下, 纳米流体的对流换热随着粒径的增大而减弱; 在相同的Ra数和粒径下, 纳米流体的对流换热随着体积分数增大而增强. 关键词： 纳米流体 Raleigh-Benard 多相流 格子Boltzmann方法     

用晶格玻尔兹曼方法研究颗粒在涡流中的运动

用晶格玻尔兹曼方法研究小颗粒在涡流中的运动.涡流由流经空腔的流体产生.用动量交换法和压力张量积分法计算颗粒在涡流中的运动轨迹、速度和角速度.最后用张量积分法计算两个不同半径的颗粒在涡流中的运动. 关键词： 晶格玻尔兹曼方法 涡流 颗粒     

非球形颗粒布朗运动的涨落-格子Boltzmann数值研究

采用涨落-格子Boltzmann方法对非球形颗粒(二维)的布朗运动进行直接数值模拟.数值结果包括椭圆形、矩形颗粒的速度均方值及速度自相关函数等.研究发现,对于非球形颗粒,其方向性并没有影响能量均分原理的适用性,每个自由度的能量由其速度或角速度的均方值确定,而且计算的颗粒平动温度和转动温度一致.此外,颗粒的速度自相关函数在相对长的时间内以~ct^-1的规律衰减,其系数c与颗粒的形状无关.     

Test of the Possible Application of the Half—Way Bounce—Back Boundary Condition for Lattice Boltzmann Methods in Complex Geometry

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes,The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries,In this paper,we test the possible application of the half-way bounce-back rule to the system with complex geometry,Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.     

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L₂-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L₂-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.     

Lattice Boltzmann simulation of the two-dimensional flow of a magnetic suspension between two parallel walls under a non-uniform magnetic field

We have developed a lattice Boltzmann method based on fluctuation hydrodynamics that is applicable to the flow problem of a particle suspension. In this method, we have introduced the viscosity-modifying method, rather than the velocity-scaling method, in which a modified viscosity is used for generating random forces in lattice Boltzmann simulations. The viscosity-modifying method is found to be applicable to the simulation of a magnetic particle suspension. We have applied this method to the two-dimensional Poiseuille flow of a magnetic suspension between two parallel walls in order to investigate the behavior of magnetic particles in a non-uniform applied magnetic field. From the results of the snapshots, the pair correlation function between the magnetic pole and the magnetic particles and the averaged local particle velocity and magnetization distributions, it was observed that the behavior of the magnetic particles changes significantly depending upon which factor dominates the phenomenon in the balance between the magnetic particle–particle interaction, the non-uniform applied magnetic field and the translational and rotational Brownian motion.     

Lattice Boltzmann Study of a Vortex Ring Impacting Spheroidal Particles

Interaction of vortex rings with solid is an important research topic of hydrodynamic. In this study, a multiple-relaxation time (MRT) lattice Boltzmann method (LBM) is used to investigate the flow of a vortex ring impacting spheroidal particles. The MRT-LBM is validated through the cases of vortex ring impacting a flat wall. The vortex evolution due to particle size, the aspect ratio of a prolate particle, as well as Reynolds $(Re)$ number are discussed in detail. When the vortex ring impacting a stationary sphere, the primary and secondary vortex rings wrap around each other, which is different from the situation of the vortex ring impacting a plate. For the vortex ring impacting with a prolate spheroid, the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle. However, it is found that after the vortex wrapping stage, the primary vortex recovers along the short axis of the particle faster than that in the long axis, i.e., the primary vortex ring stretches mainly along the short axis of the particle. That has never been addressed in the literature.     

振动纤维捕集颗粒的格子Boltzmann模拟

采用格子Boltzmann方法对振动纤维捕集颗粒进行数值研究.纤维附近采用多块网格加细技术计算,颗粒采用Lagrange跟踪方法模拟.研究雷诺数为200的流向振动纤维绕流的AⅡ、AⅢ、AIV、S四种涡结构下的亚微米煤粉颗粒的捕集问题.结果表明纤维的流向强迫振动能够显著提高颗粒的捕集效率.且迎风面的捕集效率提升不大,背风面的提升则更为显著.颗粒撞击角度的统计反映了背风面捕集效率提升的细节.另外流动处于AⅢ模态时,每个周期内脱落两个正涡一个负涡,被捕集颗粒的初始位置分布不对称.而其它模态基本关于流场中心对称.     

On the energy per particle in three- and two-dimensional Wigner lattices

We come back to the 1979 controversy about the value of the energy per particle, in an infinite Wigner lattice of electrons in a uniform compensating background. For simplicity we restrict ourselves to the simple cubic (and square) lattice. We present an accurate calculation of the energy _el of one electron in the field of the other electrons plus background for the case that the system (system I) is considered as an infinite arrangement of neutral cubes (Wigner-Seitz cells). The value obtained is checked by computer calculations. We confirm the conclusion of de Wette that for this system the relation _i=1/2 _el (often accepted without discussion) does not hold and we calculate the difference, which represents the average potential in the system. On the other hand, if the system is considered as the limit of a set of spheres with increasing radii, such that the spheres are neutral (system II), we obtain a different value of _el and in this case _i=1/2 _el. We show explicitly that the Ewald method of summation, used by Fuchs and others, leads to the same analytical expression as the limit obtained for a set of neutral spheres (system II). We extend the calculations to the two-dimensional square lattice. Here the equality _i=1/2 _el holds also in the case of an infinite arrangement of neutral squares (system I).This paper is dedicated to our friend and colleague Nico van Kampen in honor of his lifelong dedication to science in general and to theoretical physics in particular.     

惯性颗粒所见被动标量统计特性的DNS与模型研究

本文采用DNS方法,对惯性颗粒所见各向同性湍流中具有平均标量梯度的被动标量场统计特性进行了研究。结果表明：惯性对颗粒温度脉动强度,两相温度关联,自相关特性以及颗粒热流与两相交叉热流的统计特性具有明显的影响。在PDF方法的框架下,系统地推导了非等温气固两相流的PDF方程,且基于朗之万随机体系对方程进行了封闭,并利用前面的...     

介观尺度通道内多相流动的耗散粒子动力学模拟

采用四次方光滑函数构造了包含远程吸引近距排斥的保守力势函数, 应用该势函数, 采用耗散粒子动力学方法, 对十字型微通道内的多相流动进行了计算. 计算结果表明, 该势函数能有效模拟十字型微通道内的流动过程及模式. 关键词： 多相流 耗散粒子动力学 保守力势函数